The energy of the electric field

Talking about what the energy of an electric field is, one can not fail to point out that this is its most important parameter. Despite the fact that the very term "energy" is quite familiar and, at first glance, it is obvious, in this case it is necessary to understand well what is being said. For example, as is known, the energy of the electric field can be measured from any arbitrary level of it, conditionally taken as the origin (that is, zero). Although this gives some flexibility in the preparation of calculations, an error can lead to calculations of a completely different energy. This point we will clarify a little later, using the formula.

The energy of the electric field is directly related to the interaction of two or more point charges. Consider an example with two charges - q1 and q2. The potential energy of the electric field (in this case - electrostatics) is defined as:

W = (1/4 * Pi * E0) / (q1 * q2 / r),

Where E0 is the strength, r is the distance between the charges, Pi is 3.141.

Since the field of the former acts on the second (and vice versa), we determine the potentials of these fields. The first charge affects the second:

W = 0.5 * (q1 * Fi1 + q2 * Fi2).

In this formula (we denote it by 1) there are two new quantities - Fi1 and Fi2. Let us calculate them.

Fi1 = (1/4 * Pi * E0) / (q2 / r).

Respectively:

Fi2 = (1/4 * Pi * E0) / (q1 / r).

Now the first important point: the formula "1" contains two terms (q * Fi), actually representing the charge interaction energy and the coefficient 0.5. However, the energy of the electric field is not part of any charge, therefore, to take into account this feature, you need to enter the correction "0.5".

As already indicated, the interaction has several charges on each other (not necessarily just two). In this case, the energy density of the electric field is higher. Its value can be found by summing the data obtained for each pair.

Now let us return to the problem of choosing the origin referred to at the beginning of the article. Thus, it follows from the formulas that if the calculations are carried out with respect to arbitrary points, the distance from the charges tends to infinity, the result will be the value of the work done by the field, carrying charges from each other to an infinite distance. But if you want to know the value of the field work, spent for a relatively small movement of the charges themselves, then the reference point can be chosen either, since the value obtained as a result of calculations does not depend on the choice of the reference point.

Let us give an example of how this can be used in practical calculations. For example, there are three charges, the spatial configuration of which is a triangle. The distances (r) between q1, q2 and q3 are equal.

Calculate the potential:

Fi = 2 * (q / 4 * Pi * E0 * r).

Now we can determine the interaction energy of the charges themselves:

W0 = 3 * ((q * q) / 4 * 3.141 * E0 * r).

This is exactly the work that will be done when moving to an infinite distance.

If the displacement of all three occurs from the common center by the same amount, then a triangle with sides r1 (against the previous r) is formed.

We define the energy:

W = 3 * ((q * q) / 4 * Pi * E0 * r1).

In this case, we can speak of a decrease in the total energy of the entire system of three charges. It is worth noting that if r1 (r) tends to infinity, then the original energy and the work produced become equal.

We complicate the problem and remove from the system one arbitrary charge. As a result, we obtain a classical case with two charges located at a distance r.

The energy of such a system is:

W = (q * q) / (4 * Pi * E0 * r).

And the field itself will perform the work on the movement, numerically equal to:

A = 2 * ((q * q) / 4 * Pi * E0 * r).

Further all is simple: removal of one more charge will lead to that total energy becomes zero (there is no distance). In this case, the work and the field are numerically equalized. In other words, the original energy is completely transformed into work.

Calculations related to the determination of energy for an electric field are usually applied to the selection of capacitors. After all, each such device is two plates separated by a distance r, on each of which the charge is concentrated.